**Handout #23**** - Transformers**

A transformer is a simple device which changes electrical energy of a given voltage into electrical energy at *a different* voltage level. It consists of two coils which are *not* electrically connected, but which are arranged in such a way (see diagram) that the magnetic field surrounding one coil cuts through the other coil by being directed along an iron core.

When an ** alternating** (AC) voltage is applied to one coil, a magnetic field oscillation is created around that coil. The magnetic field builds and expands, then shrinks to essentially nothing, then expands again in the

*opposite*direction, then shrinks again, making a complete cycle. This varying magnetic field set up around that coil is strengthened by the presence of the iron core, and most of the magnetic field lines end up oscillating within the iron core. Because the second coil is wrapped around the iron core, the oscillating magnetic field creates an alternating voltage (at the same frequency) in the other coil by mutual induction. A transformer can also be used with pulsating DC (direct current), but a pure DC voltage that is

*not*pulsed cannot be used, since only a

*varying*voltage creates the varying magnetic field which is the basis of the mutual induction process. When DC current is connected to a coil of wire, the magnetic field is established, but does not change, creating only a momentary spike in the voltage in the second coil.

A transformer consists of three basic parts, as shown. The construction of a transformer includes a ferromagnetic (usually iron) core around which multiple coils, or windings, of wire are wrapped. The input line (the one connected to your power source) connects to the 'primary' coil, while the output lines connect to the 'secondary' coil, which has

*a different number of windings*. Energy is transferred by inductance from the primary to the secondary coil. The energy transfer is not 100% efficient: the sum of the output power must equal the sum of the input power minus losses. Energy losses in transformers are due to a number of factors: these are copper losses in the coils themselves due to material resistance, core losses due to hysteresis (the reluctance of the material's magnetic domains to reverse during each electrical cycle), leakage flux (when some magnetic field lines lie outside the core), and eddy currents.

In an ideal transformer (which had no losses), the input power must equal the output power: 40 watts in, 40 watts out. This leads to an interesting discovery when we realize that the power is equal to the current times the voltage (P = IV), and that this relation applies to both coils separately:

P1 = I1V1 and P2 = I2V2, but because P1 must equal P2, we see that I1V1 = I2V2. In other words, if 4 amps at 10 volts is applied to the primary (40 watts of power), the secondary coil must also have 40 watts of power. But 40 watts of power can arise from 4 amps at 10 volts, 2 amps at 20 volts, 1 amp at 40 volts, or with any other combination that yields 40 watts! How do we know what the current and voltage will be in the secondary coil? It turns out that the *voltage* depends upon the ratio of the number of windings (N) in the primary and secondary coils:

V1/V2 = N1/N2 or equivalently: V1/N1 = V2/N2

So if the number of windings in the secondary coil (N2) is equal to the number of windings in the primary coil (N1), then their voltages must be the same. If the voltages are the same, then their current must also be the same to yield the same power.

If there are twice as many windings on the secondary coil, then the voltage must double, but in order for the power to stay constant, it must be halved! Or if the number of windings on the secondary coil is half as many as on the primary, the current must double to keep the power constant.